A short proof of the characterization of model sets by almost automorphy

TL;DR

This paper provides a simple proof showing that repetitive model sets can be characterized as repetitive Meyer sets with an almost automorphic dynamical system, clarifying their structural properties.

Contribution

It offers a straightforward demonstration of the characterization of repetitive model sets via almost automorphy, simplifying previous complex proofs.

Findings

Repetitive model sets are characterized by almost automorphy.

Repetitive Meyer sets with almost automorphic systems correspond to model sets.

The proof simplifies understanding of the structure of model sets.

Abstract

The aim of this note is to provide a conceptually simple demonstration of the fact that repetitive model sets are characterized as the repetitive Meyer sets with an almost automorphic associated dynamical system.